On many small tractors a special diode is incorporated into the wiring harness. Typically called a flyback diode.
Its job is to block what is called back electromotive force, generated by things like the coil in a starter solenoid which sends a pulse of high voltage backwards into the electrical system as it shuts off.
If for example the battery was boosted and the cables, even momentarily, connected backwards this diode can be blown.
Once the diode is blown it becomes a dead short in the main electrical system.
I have seen a Kawasaki engine, which is what you have, installed on a Toro zero turn and the flyback diode was blown when a new battery was installed with the cables reversed.
Locating and then removing the diode for a short time will confirm if this is the cause as a new fuse will no longer blow.
If handy you can buy a suitable diode at a big electronics place and cut open the factory rubber case and solder it in.
Here is a Kohler wiring diagram showing the flyback diode. Other engine makes are similar.
The following picture shows the factory diode cut open to expose the internal electronic component.
It looks like a two pin trailer wiring harness type connector that just plugs into the wiring harness.
Sorry my photo is not clearer.
If you decide to replace the diode you need to take great care to respect the polarity on the new diode so that it matches the old one.
This diode cost about $6. It is higher rated than factory one which is fine.
Dave M7040